x-2/5x=510

Solution for x-2/5x=510 equation:

x-2/5x=510

We move all terms to the left:

x-2/5x-(510)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-510*5x-2=0

Wy multiply elements

5x^2-2550x-2=0

a = 5; b = -2550; c = -2;
Δ = b2-4ac
Δ = -25502-4·5·(-2)
Δ = 6502540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6502540}=\sqrt{484*13435}=\sqrt{484}*\sqrt{13435}=22\sqrt{13435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2550)-22\sqrt{13435}}{2*5}=\frac{2550-22\sqrt{13435}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2550)+22\sqrt{13435}}{2*5}=\frac{2550+22\sqrt{13435}}{10}
$